Session Q01: Suspensions: Rheology

Shear thinning rheology in a concentrated suspension of fibers: the role of attractive interactions

Fiber-reinforced composites are ubiquitously encountered in the engineering, automobile, and aerospace industries. Fabrication of these composites requires the mixing of fibers dispersed in a liquid, and the final structure is affected by fiber properties, interactions, and flow fields. A good understanding of the rheology of fiber suspensions can aid in the design and optimization of the fabrication processes. To this end, we simulate the simple shear flow of fiber suspensions by accounting for short-range lubrication, van der Waals attractive, electrostatic repulsion interactions, as well as friction between fibers. Direct numerical simulations are performed using the Immersed Boundary Method where the fibers are modeled as flexible slender bodies governed by the Euler-Bernoulli beam theory and the fluid flow is resolved using the Navier-Stokes equations. The simulation results for the suspension viscosity and yield stress are consistent with the experimental data from the literature for polyamide fiber suspensions. The shear-thinning behavior becomes stronger as we increase the magnitude of attractive interactions. Furthermore, we perform a parametric study varying fiber flexibility, volume fraction, aspect ratio, inertia and examine suspension viscosity and yield stress.   

Unifying disparate rate-dependent regimes in non-Brownian suspensions

A non-Brownian suspension undergoes shear thinning (decreasing viscosity) at low shear rates followed by a Newtonian plateau (constant viscosity) at intermediate shear rates which transitions to shear thickening (increasing viscosity) beyond a critical shear rate/stress and finally, a second shear-thinning transition is observed at extremely high shear rates. We quantitatively unify all the disparate non-Newtonian regimes and the corresponding transitions with increasing shear rates. Direct comparison with experimental data from the literature corroborates the validity of the model. Inclusion of traditional hydrodynamic, DLVO, and contact forces with constant friction reproduce the initial thinning and the shear thickening transition. However, to quantitatively capture the intermediate Newtonian plateau and the second shear thinning, an additional non-hydrodynamic interaction of non-DLVO origin and a decreasing coefficient of friction, respectively, are essential; thus, providing the first explanation for the Newtonian plateau along with reproducing the second shear thinning in a single framework. We demonstrate the model versatility in predicting a variety of other rate-dependent behaviors, normal stress differences, and particle tribology effects on suspension rheology.   

Experimental study of magnetorheological fluids formed used particle mixtures

The viscosity of magnetorheological (MR) fluids, which are formed by suspending particle mixtures in ferrofluids, increases within a few milliseconds of a magnetic field being applied, and goes back to the original value once the magnetic field is removed. Thus, MR fluids are appropriate for applications in which adjustable viscosity with a short response time is desired. The viscosity increases when the magnetic field is applied as a fraction of the particles become positively magnetized, while the rest are negatively magnetized. These dipoles then interact to form chains and columns aligned in the field’s direction and in the perpendicular plane. This work aims to study the dependence of the magnetorheological response on the properties, proportions, and size distribution of the particles.    

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Suspensions of hydrodynamically interacting particles are important model systems for a range of natural and industrial problems, such as protein transport in tissues or rational design of novel metamaterials, thus understanding their dynamics and rheology is of key importance. Most natural and industrial flows are time-dependent; so, it is particularly relevant to examine the suspension behaviour when it is driven periodically. Recent work in the literature have identified two mechanisms for non-colloidal suspensions of spherical particles to undergo reversible-irreversible transitions in oscillatory shear, due to either interparticle collision or attraction. However, none of the studies has included long-range hydrodynamic interactions, which may be crucial to the transient dynamics of the system. Here, we numerically examine the suspension dynamics and rheology with full hydrodynamic interactions using a newly developed fast Stokesian dynamics method. The effect of particle geometry, modelled from rigidly connecting spherical beads into composites, will also be discussed.   

Effects of volume fraction and particle shape on the rheological properties of oblate spheroid suspensions

Coupled lattice Boltzmann and discrete element methods were employed to investigate the rheological properties of oblate spheroid suspensions in a Newtonian fluid. The volume fraction of the particles is varied, along with the particle aspect ratio. As the particle shape is varied from sphere to oblate, we observe an increase of the relative viscosity, as well as an increase of the particle contacts and the contact distance. We also report the first and second normal stress difference coefficients as they vary with the volume fraction and/or the particle shape. The more oblate particles in denser suspensions are observed to reorient systematically subject to the shear flow. We recast the viscosity data using the Krieger-Dougherty formula and report the modified Einstein coefficients.   

Rheology of dense, bidispersed suspensions: Segregative phenomenon induced by a flow perturbation

We have studied the phenomenon of segregation of a non-Brownian dense suspension (volume fraction φ = 0.5) of rigid, inertialess, neutrally buoyant, bidispersed particles, with a large particle-size-ratio a2/a1 = 3, being a1 and a2 the radii of the smaller and larger particles in the suspension, respectively. The particles have been immersed in a plain shear-flow of a Newtonian-fluid at a low Reynolds number. The shear-rate was varied to analyse the whole rheological behaviour of the suspension. To induce the segregation of the larger particles from the smaller ones, we perturbed the underline shear flow by adding a simple sinusoidal wave to the streamwise velocity, with the wavy-variations in the direction of the shear. We carried out a parametric study varying the amplitude and the wavenumber of the sinusoidal disturbance to analyse their relative importance in the onset of the phenomenon of segregation. The study has been performed by means of numerical simulations that tackle the Newton-Euler equations governing the dynamics of the particles. Preliminary results show that the larger particles tend to migrate towards the regions of minimum shear if the amplitude of the perturbation is above a threshold limit. An increasing wavenumber can help to segregate the particles.   

Experimental evidence of viscous-inertial transition in non-colloidal granular suspensions

Dense granular suspensions can exhibit different regimes depending on the boundary conditions and stress distribution. In general, the flow is mainly controlled by the ratio of the shear rate and the particle pressure, which could be partially well described by a frictional approach for a dilatant granular media. However, as the shear rate increases and the fluid viscosity decreases, the flow can transit from a viscous to an inertial regime. In absence of constitutive equations, dimensional analysis does not give the crucial information to determine this transition, and except for some numerical works, there is not substantial experimental evidence of this phenomenon. 

In the present work, we present an experimental evidence of the viscous-inertial transition for suspension of non-colloidal rigid particles. A specially  designed pressure-and-volume imposed rheometer is used to explore the dense regime. By varying systematically the interstitial fluid, the shear rate, and packing fraction, we show that the transition takes place at a specific Stokes number, which is independent of the packing fraction. The algebraic power law for the viscosity divergence is also shown to be independent of the regime   

Rheology of mobile sediment beds sheared by viscous, pressure-driven flows

We present a detailed comparison of the rheological behaviour of sheared sediment beds in a pressure-driven, straight channel configuration based on data that was generated by grain-resolved direct numerical simulations and the experimental measurements of Aussillous et al. (J. Fluid Mech., vol. 736, 2013, pp. 594-615). The highly-resolved simulation data allows to compute the stress balance of the suspensions and the stress exchange between the fluid and particle phase. Using this knowledge, we obtain the depth-resolved profiles of the relevant rheological quantities. The scaling behavior of these quantities are examined and compared to data coming from rheometry experiments. We show that rheological properties that have previously been inferred for annular Couette-type shear flows with neutrally buoyant particles still hold in the dense regime for our setup of sediment transport in a Poiseuille flow. Subdividing the total stress into parts from particle contact and hydrodynamics suggests a critical particle volume fraction of 0.3 to separate the dense from the dilute regime. In the dilute regime, i.e., the sediment transport layer, long-range hydrodynamic interactions are screened by the porous medium and the effective viscosity obeys the Einstein relation.   

Physical aging in aqueous nematic gels of a swelling nanoclay: Sol (phase) to gel (state) transition

Aqueous suspensions of geometrically anisometric, nano-sized sodium-montmorillonite (Na-Mt) display a sol–gel transition at very low solids concentrations. The microstructure of the gel formed at very low ionic strengths is considered electrostatically repulsive with a nematic character, and the gel state at ionic strengths where Debye length is of the order of particle size is conjectured to be free of physical aging. We investigated the nature of osmotically prepared Na-Mt suspensions at low ionic strength (~10-5 M), below and above the gel point. The sol phase exhibited very low yield stress than the gel state, without any sign of physical aging, thus behaving as an equilibrium state. In contrast, the gel exhibited signatures of physical aging, that is, an evolving microstructure that consolidated with time when left undisturbed thus behaving as out of equilibrium state. The physical aging behaviour became more pronounced at Na-Mt concentrations far above the gel point. A critical shear rate existed, below which no stable flows were possible in the gel state representing the microstructural reorganization timescale. Overall, Na-Mt suspensions in the gel state behave like systems that were out of equilibrium with an ever-evolving microstructure, in opposition to the assumption that low ionic strength Na-Mt gels are in an equilibrium phase. The possible origin of physical aging, such as the reversible orientation of Brownian anisotropic particles, stiffening of an existing microstructure, or reorganization of microstructure towards minimal energy configuration is discussed in detail.   

Single-particle stress for a graphene particle

We studied the dynamics of graphene freely-suspended in simple shear flow, using a combination of molecular dynamics simulations and boundary integral simulations. Graphene is  a plate-like colloidal particle, whose nanoscopic thickness is comparable to that of a typical liquid solvent molecule. Unusual for plate-like particles (e.g. clays) the thickness is also smaller than the hydrodynamic slip length characterising the relatively velocity at the fluid-solid boundary. This talk will examine the consequence of this geometric regime on the dynamics of graphene particles in shear flow, and on the ensuing rheology. For slip lengths larger than the particle thickness, the rotational dynamics predicted by Jeffery's theory ceases to occur. We recently demonstrate this behaviour by simulating 2D rigid particles that rotate only in the flow-gradient plane as well as 3D particles that have fully 3-dimensional orbits.  This effect is also seen for mildly flexible particles and for particle concentrations beyond the classical dilute regime. Our simulations also indicate a substantial drop in suspension viscosity in this slip regime.In the talk, the physical origin of the drop in viscosity will be discussed in the dilute limit for the rigid case, based on the analysis of the single-particle stresslet (moment of hydrodynamic traction) and a further integral term involving the integral of the slip velocity over the particle surface; this last term is usually ignored, as it is zero for non-slip particles, . The results show a non-trivial dependence of both these terms on the ratio of slip length and particle thickness, and on the geometric aspect ratio. We discuss whether negative contributions of the particle to the suspension viscosity are physically possible.